An inflaton mass problem in string inflation from threshold corrections to volumestabilization

Abstract

Inflationary models whose vacuum energy arises from a D-term are believed not to sufferfrom the supergravity eta problem of F-term inflation. That is, D-term models have thedesirable property that the inflaton mass can naturally remain much smaller than theHubble scale. We observe that this advantage is lost in models based on stringcompactifications whose volume is stabilized by a non-perturbative superpotential: theF-term energy associated with volume stabilization causes the eta problem to reappear.Moreover, any shift symmetries introduced to protect the inflaton mass will typically belifted by threshold corrections to the volume-stabilizing superpotential. Using thresholdcorrections computed by Berg, Haack, and Körs, we illustrate this point in the example ofthe D3–D7 inflationary model, and conclude that inflation is possible, but only forfine-tuned values of the stabilized moduli. More generally, we conclude that inflationarymodels in stable string compactifications, even D-term models with shift symmetries, willrequire a certain amount of fine-tuning to avoid this new contribution to the eta problem.